We assume that the line of sight path exists and dominates the channel between the BS and each device. In fact, the considered application is different from conventional RIS-aided networks, where in the latter an RIS is utilized to create an additional reliable channel path. In this work, the RISs are utilized to generate backscattered signals for localization and data transmission in a passive manner. We model the signal reflected by each device as a multipath characterized by an angle of propagation and a delay. Considering that there are \(K\)  devices in the service region, the delay of the \(k\) -th path is denoted by \(\tau _k\) . We assume that the localization parameters remain constant in one transmission frame consisting of \(M\)  OFDM blocks, i.e. the angles and delays do not change in the period of one transmission frame. This is reasonable, since the duration of each transmission frame is typically in millisecond, and the distance traveled by the moving device can be ignored in such a short period of time. Furthermore, since the BS transmits and receives signals at the same time-frequency slot, the interference between the transmit and receive antennas needs to be considered while modeling the echos from the devices. In this work, we assume that the receive antennas are carefully isolated from the transmit antennas, so that the self-interference can be ignored [1]}. The echos received at the BS are contaminated by an additive noise \(\mathbf {w}_m(t)\in \mathbb {C}^{N_\mathrm {r}\times 1}\)  as
\(\mathbf {y}_m(t)=\sum _{k=0}^{K-1}\beta _k\mathbf {H}_{\mathrm {UL},k}\mathbf {\Lambda }_{k,m}\mathbf {H}_{\mathrm {DL},k}\mathbf {x}_m(t-\tau _k)+\mathbf {w}_m(t),\) 
